Solve the following problems. 1. Determine the focus and directrix of the parabola with the given equation. Sketch the graph, and indicate the focus, directrix, and vertex. а. у? b. 3x2 = -12y c. x2 – 6x – 2y + 9 = 0 = 20x
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
![Solve the following problems.
1. Determine the focus and directrix of the parabola with the given equation. Sketch
the graph, and indicate the focus, directrix, and vertex.
а. у?
b. Зx2 3D —12у
с. х2 — 6х — 2у +9 %3D 0
d. 3y? + 8x + 24y + 40 = 0
= 20x
2. An object thrown from a height of 2 m above the ground follows a parabolic path
until the object falls to the ground (see figure below). If the object reaches a
maximum height (measured from the ground) of 7 m after travelling a horizontal
distance of 4 m, determine the horizontal distance between the object's initial
and final positions.
7 m
2 m](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bdf0782-6393-4b81-974d-398dea84f6ef%2F8333df52-0622-4995-9476-ad9e2a4ec2d5%2F8a67358_processed.jpeg&w=3840&q=75)
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